Quantum ElectroDynamics

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TOPIC 6Electric currentand resistance
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Electrons in Conductors

• Conductors have free electrons, which
• Are in continuous rapid motion thermal and
  quantum effects
• Undergo frequent scattering from the crystal
  lattice (positive ions)
• Random motion does not constitute a current
• An applied electric field results in a small
  drift velocity superimposed on the random motion
• This drift gives a net movement of charge an
  electric current, I

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Electric Current
Unit of current is Amp (Ampère), 1 A 1 C s1
Continuous current through conductor ? potential
difference between ends eg due to
battery Battery raises positive charges from low
potential (negative terminal) to high potential
(positive terminal) As much charge enters one end
of the conductor (eg wire) as leaves at the
other end it does not charge up! Current only
flows in a closed loop or circuit Current
density J current flow per unit area
(perpendicular to current) J I/A
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Electrical Resistance
The current I flowing through a component depends
on the potential difference between its ends,
V. We can define the resistance R of the
component from Unit of resistance ohm ? (1 ?
1 volt per amp) Conductance G 1 / R (units
?1, mho or siemens)
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Drude Model
Assume n electrons (of charge q e) per unit
volume Applied electric field E gives
acceleration Mean time between collisions with
lattice ? Drift velocity (superimposed on
random motion) Charge ?Q in dotted cylinder n
? A q, passes end plane in time ?t ?/vd, so I
n A q vd Hence
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Resistivity Conductivity

• Drude model ?
• We can write this
• ? is the resistivity, with units ? m
• 1 / ? conductivity
• Note J I / A
• V E ?

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Example 1 Resistance, drift velocity Copper has
a resistivity of 1.7?108 ? m, and 8.5 ?1028 m3
free electrons. What is the mean time between
collisions between a conduction electron and the
lattice? What will the drift velocity be when
2.0 V is applied across a 5.0 m sample of
copper? What resistance will a copper coil have
if it is formed of 1000 turns of wire, of
diameter 1.0?mm, wrapped around a tube of radius
3.0?cm?
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Temperature Coefficient of Resistivity
Increased temperature ? increased lattice
vibrations ? increased electron scattering ?
increased resistivity in most materials Approximat
ion for modest temperature changes Here ? is
the temperature coefficient of resistivity. Examp
le 2 A sample of platinum has a resistance of
30.00? at 20?C, and 39.41? at 100?C. What is the
coefficient of resistivity for platinum? What
would the resistance be at 0?C?
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Electrical Power
The energy loss of a charge Q falling through
potential difference V is Q V. The power
dissipated (rate of energy loss) is therefore P
dQ/dt V I V. Using V I R, this can be
expressed in a variety of useful ways Example
3 A resistance of 3.0 ? is connected across a
potential difference of 2.0 V. How large is the
current that flows, and how much power is
dissipated?